Questions tagged [mathematical-modeling]

This tag is used to refer to mathematical/probabilistic/statistical modeling questions, usually this tag is used to ask about questions that are related with the mathematical formalism of the model instead of the correctness of a specific model in practice.

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-4 votes
0 answers
76 views

Basic reproduction number for an epidemic model [closed]

I have a system of 6 ODE representing infected subpopulations of a model of epidemic $$ \begin{cases} \dfrac{de}{dt} =\dfrac{dy_2}{dt} = \phi y_1(y_4+y_5)-p_2 y_2\\ \dfrac{dq^*}{dt} =\dfrac{dy_3}{dt} ...
0 votes
0 answers
12 views

Understanding relation of 2 dependent, integral equations which are nested in a Bayesian Expectation

I'm trying hard to try understand the recursive nature between two equations in a recent macroeconomics paper, but my question mainly relates to how mathematically such recursive equations can depend ...
5 votes
1 answer
206 views

Equation in epidemic SIR model with the influence of vaccinations

I am currently preparing a presentation on different modifications of the SIR model. In my sources about the use of vaccines, I came across the following model for a specific rate at which the ...
0 votes
0 answers
49 views

Question on the modelling of (viscous) fluid in a bag with holes

Consider some fluid (as nice as possible) in a plastic bag with holes illustrated by the image below (of course no holes have been drawn in this picture) What is the corresponding PDE to model the ...
5 votes
3 answers
1k views

Mathematical modeling of voting/rating (e.g. political elections, questions on MO, gadgets on amazon,...)

We need to make choices in our life and so we need to compare(=rate) things what is good what is bad. Question: are there some mathematical models which may capture features of some kind of voting/...
5 votes
0 answers
234 views

How to play golf in one dimension?

One-dimensional golf is a function $g$ on $\mathbb R$ such that $g(x)= 1+\min_\mu E[g(x+N(\mu,c\mu^2))]$ if $|x|>1$ and 0 if $|x|\le 1.$ Here $N$ is the normal distribution, whose mean $\mu$ you ...
0 votes
1 answer
250 views

How to force my differential equations give a bounded solution?

I have modeled the interaction of two physical quantities, $S$ and $B$, by the following differential equations (the second one is a delay differential equation): $$S'(t) = 0.31 S(t) \Big( 1 - \frac{S(...
0 votes
1 answer
115 views

How to integrate an indicator function/constraint into the cost function of a linear program?

I have a mathematical model $P$ for which I optimize two cost functions say $F_1$ and $F_2$ subject to a set of constraints $C1$–$C10$. In $F_2$, I want it to be included only when its expression ...
30 votes
7 answers
6k views

Applications of mathematics in clinical setting

What are some examples of successful mathematical attempts in clinical setting, specifically at the patient-disease-drug level? To clarify, by patient-disease-drug level, I mean the mathematical work ...
0 votes
0 answers
35 views

Gaussian white noise model in application

I am interested in applications (to data) of non-parametric statistics, and my question concerned the Gaussian white noise model defined by, $$ X_{t_1, \ldots, t_d}=f\left(t_1, \ldots, t_d\right) d ...
0 votes
1 answer
222 views

Poisson Process x SIR model [closed]

Consider the simplest SIR model: $$S'=-a SI$$ $$I'=a SI - b I$$ $$R'=b I$$ It is known that the waiting time of an infeccious person in the compartment $I$ follows an exponential behavior with rate $b$...
1 vote
2 answers
478 views

Why should the logarithmic series distribution model the number of "Items" bought?

Suppose you're a shopkeeper in the business of selling Items. An "Item" is a thing whose only property is that the quantity that can be bought by a purchaser must be a positive integer; all ...
1 vote
0 answers
84 views

How to smoothly interpolate gravitational field between trajectories in high dimension?

I'm looking for the adequate numerical interpolation technique to solve the following problem. This is probably trivial for physicists who study gravitational fields, but I didn't find clear answers ...
1 vote
0 answers
83 views

Advice on constructing a Non-structural Flood Mitigation Model [closed]

I am not sure if this is the right site to post this. But I seek some valuable suggestions, and I believe I can get them here. At present, I am in the final semester of my BSMS Mathematics course. I ...
3 votes
0 answers
93 views

Mathematical formulation of beam: get stress/strain from forces and momentum

I'm working with static beams with Euler–Bernoulli model which ODE is $$ \dfrac{d^2}{dx^2} \left(EI \cdot \dfrac{d^2w}{dx^2}\right) = q(x). $$ With a beam along the $x$ axis, the solution consists of ...
1 vote
1 answer
82 views

Resources/Reading Materials on PASA (optimal control theory)

I am currently working on my undergraduate thesis, and my adviser suggested that I look into a Polyhedral Active Set Algorithm (PASA) for my paper. I have been trying to find resources/materials on it ...
1 vote
0 answers
78 views

Turing reaction diffusion equations and neural networks

Suppose you have a Turing-type reaction-diffusion system $$ \begin{cases} \partial_t \phi = & f(\phi, \psi) + D_\phi \nabla^2\phi \\ \partial_t \psi = & g(\phi, \psi) + D_\psi \nabla^2\psi \...
2 votes
1 answer
151 views

Mechanics: Model beam using differential vectorial formulation

At the Wikipedia there are the differential formulation for Euler-Bernoulli Beam \eqref{1} and Timoshenko Beam \eqref{2} $$ \begin{align} &\dfrac{d^2}{dx^2}\left(EI\dfrac{d^2w}{dx^2}\right) = q(x) ...
-2 votes
1 answer
785 views

Equation for bowling ball on a trampoline

I'm searching for the displacement of the surface of a elastic rectangle for a given x and y and a force at a position. Like a bowling ball on a trampoline. The equation should include a variable for ...
3 votes
0 answers
166 views

How to mix Lagrange mechanics + KKT conditions?

Question: How can I mix the concepts of Lagrange Mechanics and KKT conditions? I've learned that Lagrange Mechanics derivation comes from variational calculus, and in some formulations, we can add ...
2 votes
1 answer
347 views

Examples of ODEs with complex constant coefficients and applications to physics?

This question is asked on stackexchange: Are there examples for ODEs with complex coefficients with applications in physics? but received no answers. I am reposting it here on the hope that it catches ...
0 votes
0 answers
36 views

What is the meaning of column integrated fluxes?

I am solving an equation where one term $\bar{P}$ is given and is called the integrated column flux. In the equation, the term $P$ is the precipitation. I am doing this on the discrete domain. Anyone ...
0 votes
0 answers
27 views

How to define Mock Hadley Cell in mathematical modeling?

I am computing a force term in which one component is $F_{ext}$. To define this, the following content given in the paper. To capture the possible large-scale effects on precipitation clusters, we ...
0 votes
3 answers
613 views

Integer linear constraint(s) for y= x1 XOR x2 [closed]

Is there any way to convert $y=x_1~ \text{XOR} ~x_2$ to linear constraints? It means we write some linear relations with: if $x_1=x_2 =0$ or $x_1=x_2=1$ $\to$ $y=0$, else, $y=1$?
2 votes
1 answer
202 views

Literature on reaction diffusion equations

My research area is age structure modelling, basically when applied to reaction diffusion equations. We mainly discuss the existence of travelling wave solutions; I want to work on the stability of ...
31 votes
7 answers
3k views

Does every ODE comes from something in physics?

Not sure if this is appropriate to Math Overflow, but I think there's some way to make this precise, even if I'm not sure how to do it myself. Say I have a nasty ODE, nonlinear, maybe extremely ...
7 votes
1 answer
430 views

How to study the global stability for this 3D system?

I am studying a biological system (HIV) and arrived at this simplified dynamical system: \begin{align} x_1' &= a_1 + a_2x_2 - a_1x_2 - a_4x_1 - a_5\frac{1+a_6x_3}{1+a_7x_3}x_1\\ x_2' &= a_5\...
33 votes
8 answers
11k views

How is differential geometry used in immediate industrial applications and what are some sources to learn about it?

Intuitively it might be clear that differential geometry is a very applicable subject in engineering and industry. I'd like to know how some industries/companies use differential geometry. I'd guess ...
2 votes
0 answers
101 views

How to quantify the non-commutativity of human body motion? [closed]

Some years ago, there was that question on this forum:"How to quantify noncommutativity?". I am asking that question in a context, human movement, which implies kinematic chains (like in ...
5 votes
1 answer
3k views

How can I generate the simulated time series

I am curious how one can generate simulated time series data. I found a list of simulated series here and a similar tool for stock market. What is the best way to generate domain specific time series ...
3 votes
0 answers
368 views

How to promote a blog?

Math behind might be interesting. Quite recent bloggingg activity might have interesting math model. The point is that bloggers compete for subscribers and at the same time cooperate gaining ...
1 vote
0 answers
77 views

Real life applications of distributions through models or simulations [closed]

What are the areas we can apply distributions in classical harmonic analysis? I don't mean probability distributions but distributions that are continuous linear functionals on the space of test ...
6 votes
1 answer
291 views

Current status on Richardson's model (growth model)

A very simple stochastic growth model on a lattice is the Richardson's model (Actually originally defined by Murray Eden in the 60s). Each point of the lattice can be either occupied or vacant, once ...
2 votes
1 answer
135 views

Reference request: probabilistic models on climate (change)

I am looking for probabilistic models to address climate change. Are they known in the existing literature? I have found the post Math behind climate modeling. concerning PDE models. Many thanks for ...
1 vote
0 answers
73 views

Canonical representation of the a probability distribution for Hammersley Clifford Theorem

I'm reading the following paper http://www2.stat.duke.edu/~scs/Courses/Stat376/Papers/GibbsFieldEst/BesagJRSSB1974.pdf On page 7 they give the result that $$Q(\textbf{x}) = \sum_{1 \leq i \leq n} ...
3 votes
0 answers
110 views

Image restoration quality general lower bounds

A typical image restoration model posits that, starting from a true image $f = f(x,y)$, we observe $$ \tilde f = f \star h + n $$ where $\star$ is convolution, $h$ is the point spread function (caused,...
1 vote
0 answers
87 views

Discrete-time model for spread of information when the probability of information transfer between each pair is known

[This question is cross-posted from MSE.] I'm interested in the behaviour of the following sort of system. We are given: a finite set $X$, a subset $A_0 \subset X$, and a function $f : X \times X \to [...
6 votes
1 answer
485 views

Graphs resembling the math genealogy graph must have concentration in a small number of families?

I was talking with a non-mathematician the other week at a workshop about the fact that many mathematicians, like myself, are indexed in the math genealogy database. We talked a little about how many ...
2 votes
1 answer
83 views

Introductory literature on the Voter Model

I am looking for a good introduction to the voter model appropriate for the Bachelor-Maths level (Europe). I need something that introduces the model on a low level, as a Glauber dynamics or similar. ...
2 votes
1 answer
368 views

Logistic sequence convergence

1) How can we prove that the logistic sequence $$x_{n+1}=rx_n(1-x_n),\ x_1=a\in (0,1)$$ converges to $\frac{r-1}{r}$, for $r\in [1,3]$? 2) Also I wonder how can we prove that the sequence $(x_n)_{n\in\...
3 votes
1 answer
151 views

What is the ideal form of an h-curve?

This question concerns mathematical modelling of the citation curve, well-known in the sciencemetry. The citation curve (or else the $h$-curve) of an individual researcher is the vector $(c_1,c_2,\...
8 votes
4 answers
1k views

Virus community spread mathematical modeling [closed]

What is the basic math behind the Virus community spread mathematical modeling,and how the time variable;(in these models),interacts with knowledge (data)?. I am not asking about how the virus is ...
5 votes
1 answer
689 views

Generalized linear models: What's the benefit of the underlying theory?

I was recently trying to understand generalized linear models (GLMs) and after investing quite a few days, it still hasn't dawned on me what the fundamental benefit of the framework is. Normally, I am ...
1 vote
1 answer
280 views

How many persons pass your 1.5 meter neighbourhood during 1 week ? If the distribution is power law what is the exponent?

Consider a graph with vertices being people (in some region), and make an edge if one person pass another closer than say 1.5 meter during say one week. (Such a graph might be thought a kind of ...
3 votes
0 answers
130 views

Notions of "completeness" and "sufficiency" of a mathematical model

I'm modelling a real-world problem as having instances $i$ in a set $P$. As a very simple artificial example, consider the problem of choosing a meeting room given a certain number of people. Then $i =...
6 votes
1 answer
274 views

Time of peak of an SIR epidemic

I've learned some classical results on the peak and the attack rate of an idealized epidemic which evolves according to a SIR model $\dot{s} = -\beta\cdot i \cdot s$ $\dot{i} = +\beta\cdot i \cdot s -...
1 vote
0 answers
125 views

Next-generation matrix of infectious disease

If the population is classified into $\mathbf{S}$, $\mathbf{E}$, $\mathbf{I}$ and $\mathbf{R}$ compartments such that \begin{equation} \label{eq4} \begin{aligned} \mathbf{S} &=\dfrac{S_{1}N_{1}+...
4 votes
1 answer
2k views

How to mathematically characterize a feedback loop in ODEs?

I have a biological system that exhibits a feedback type of behavior. The diagram is a schematic of the system of ODEs. In this system, the total amount of $x_1, x_2, x_3$ is conserved; however, there ...
6 votes
2 answers
294 views

Searching for an early, highly theoretical, even philosophical, math paper on models or small-world networks

All I can remember is that it was very high-level / abstact and kind of philosophical, explaining (the discovery or interdependence of) small world networks. I assume that it was +50 years old and '...
4 votes
2 answers
260 views

Approximated solutions of SEIR models

Numerical solutions of the SEIR equations (describing the spreading of an epidemic disease) – or variations thereof – $\dot{S} = - N$ $\dot{E} = + N - E/\lambda$ $\dot{I} = + E/\lambda - I/\delta$ ...